# laed5 - Man Page

laed5: D&C step: secular equation, 2x2

## Synopsis

### Functions

subroutine **dlaed5** (i, d, z, delta, rho, dlam)**DLAED5** used by DSTEDC. Solves the 2-by-2 secular equation.

subroutine **slaed5** (i, d, z, delta, rho, dlam)**SLAED5** used by SSTEDC. Solves the 2-by-2 secular equation.

## Detailed Description

## Function Documentation

### subroutine dlaed5 (integer i, double precision, dimension( 2 ) d, double precision, dimension( 2 ) z, double precision, dimension( 2 ) delta, double precision rho, double precision dlam)

**DLAED5** used by DSTEDC. Solves the 2-by-2 secular equation.

**Purpose:**

This subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO * Z * transpose(Z) . The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j . We also assume RHO > 0 and that the Euclidean norm of the vector Z is one.

**Parameters***I*I is INTEGER The index of the eigenvalue to be computed. I = 1 or I = 2.

*D*D is DOUBLE PRECISION array, dimension (2) The original eigenvalues. We assume D(1) < D(2).

*Z*Z is DOUBLE PRECISION array, dimension (2) The components of the updating vector.

*DELTA*DELTA is DOUBLE PRECISION array, dimension (2) The vector DELTA contains the information necessary to construct the eigenvectors.

*RHO*RHO is DOUBLE PRECISION The scalar in the symmetric updating formula.

*DLAM*DLAM is DOUBLE PRECISION The computed lambda_I, the I-th updated eigenvalue.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

Definition at line **107** of file **dlaed5.f**.

### subroutine slaed5 (integer i, real, dimension( 2 ) d, real, dimension( 2 ) z, real, dimension( 2 ) delta, real rho, real dlam)

**SLAED5** used by SSTEDC. Solves the 2-by-2 secular equation.

**Purpose:**

This subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO * Z * transpose(Z) . The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j . We also assume RHO > 0 and that the Euclidean norm of the vector Z is one.

**Parameters***I*I is INTEGER The index of the eigenvalue to be computed. I = 1 or I = 2.

*D*D is REAL array, dimension (2) The original eigenvalues. We assume D(1) < D(2).

*Z*Z is REAL array, dimension (2) The components of the updating vector.

*DELTA*DELTA is REAL array, dimension (2) The vector DELTA contains the information necessary to construct the eigenvectors.

*RHO*RHO is REAL The scalar in the symmetric updating formula.

*DLAM*DLAM is REAL The computed lambda_I, the I-th updated eigenvalue.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

Definition at line **107** of file **slaed5.f**.

## Author

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